通过Maslov指数透镜的不稳定性分叉
Bifurcation to instability through the lens of the Maslov index
摘要：
Maslov指数是评价孤波稳定性的有力工具。虽然一般情况下很难计算，但最近为奇异摄动系统建立了一个计算框架。在本文中，我们应用这个框架的驻波解的三个组件的激活剂-抑制剂模型。已知这些驻波随着参数变化而变得不稳定。我们的目标是看看这个既定的稳定性标准如何体现在马斯洛夫指数计算。通过这样做，我们对不稳定性的机制有了新的认识。我们进一步建议如何使用这种机制来揭示新的不稳定性奇摄动模型。
英文摘要：
The Maslov index is a powerful tool for assessing the stability of solitary waves. Although it is difficult to calculate in general, a framework for doing so was recently established for singularly perturbed systems. In this paper, we apply this framework to standing wave solutions of a three-component activator-inhibitor model. These standing waves are known to become unstable as parameters vary. Our goal is to see how this established stability criterion manifests itself in the Maslov index calculation. In so doing, we obtain new insight into the mechanism for instability. We further suggest how this mechanism might be used to reveal new instabilities in singularly perturbed models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
